370. Вычислите значение корня:

Решение:

а) \(\sqrt{\frac{9}{64}}\)

1. \(\sqrt{\frac{9}{64}} = \frac{\sqrt{9}}{\sqrt{64}} = \frac{3}{8}\)

б) \(\sqrt{\frac{36}{25}}\)

1. \(\sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5}\)

в) \(\sqrt{\frac{121}{25}}\)

1. \(\sqrt{\frac{121}{25}} = \frac{\sqrt{121}}{\sqrt{25}} = \frac{11}{5}\)

г) \(\sqrt{2\frac{7}{81}}\)

1. \(\sqrt{2\frac{7}{81}} = \sqrt{\frac{2 \cdot 81 + 7}{81}} = \sqrt{\frac{162 + 7}{81}} = \sqrt{\frac{169}{81}} = \frac{\sqrt{169}}{\sqrt{81}} = \frac{13}{9}\)

д) \(\sqrt{5\frac{1}{16}}\)

1. \(\sqrt{5\frac{1}{16}} = \sqrt{\frac{5 \cdot 16 + 1}{16}} = \sqrt{\frac{80 + 1}{16}} = \sqrt{\frac{81}{16}} = \frac{\sqrt{81}}{\sqrt{16}} = \frac{9}{4}\)

е) \(\sqrt{1\frac{9}{16}}\)

1. \(\sqrt{1\frac{9}{16}} = \sqrt{\frac{1 \cdot 16 + 9}{16}} = \sqrt{\frac{16 + 9}{16}} = \sqrt{\frac{25}{16}} = \frac{\sqrt{25}}{\sqrt{16}} = \frac{5}{4}\)

Ответ: а) \(\frac{3}{8}\); б) \(\frac{6}{5}\); в) \(\frac{11}{5}\); г) \(\frac{13}{9}\); д) \(\frac{9}{4}\); е) \(\frac{5}{4}\).